In modeling association between chemical exposures and health outcomes, it is often desired that an optimal combination of the chemical concentrations under consideration can be estimated, in the sense that this combination provides the best power in disease detection and prediction. However, standard approaches in the literature have been limited to several exposures. Dr. Chen plans to explore sparse estimation in the context of optimal exposure combinations. In particular, he will investigate the possibility of using penalized maximum likelihood in optimal combination estimation. In essence, this amounts to starting with a large number of potential exposures that can be used in the optimal combination, shrinking those with small effects to have zero coefficients, and dropping them out of the final optimal combination. Dr. Chen will also explore the possibility of using rank likelihood, as it allows more flexible distributional assumptions of the concentrations. Other features of the concentrations, such as limit of detection and excessive zeros, can be considered in the same framework. Although penalized maximal likelihood approaches are useful in simultaneous parameters estimation and model selection, it is possible that concentrations with nonzero associations with the health outcome can still be numerous and have small coefficients even after regularization. These small coefficients are difficult to estimate and can create computational stability problems in estimation. For these reasons, it is of interest to explore simultaneous regularization and smoothing in these analyses. The regularization part will be carried out using penalized maximum likelihood so that those with very small coefficients will be dropped out of the final models; the smoothing will be achieved through hierarchical modeling using appropriate correlation structure, similar to ideas used in spatial modeling.